The present invention relates to the measurement of the bending stiffness of sheet materials, and more particularly, to the measurement and control of the bending stiffness of paperboard as the board is being manufactured.
Bending stiffness is one of the critical parameters involved in the manufacture of many sheet materials. In the paperboard industry, for example, virtually all paperboard is sold with a bending stiffness specification. Board stiffness is important in the carton-manufacturing process and to the quality of the resulting carton. The proper board stiffness reduces jamming of the board in carton-forming machines by maintaining flat panels as carton blanks are folded. Stiff board also provides the necessary protection of carton contents. Thus, acceptance of a manufacturer's paperboard depends on the manufacturer's ability to meet the desired bending stiffness specifications.
Moreover, paperboard manufacturing is a high speed continuous process. Thus, large amounts of substandard board can easily be produced before subsequent laboratory measurements reveal that the manufactured board is unsuitable for its intended purpose. Consequently, it would be desirable to measure bending stiffness "on-line" as the board is being manufactured in order to avoid wasting time and material.
Several factors make the measurement of paperboard bending stiffness "on-line" difficult. First, the bending stiffness of paperboard varies across the width of the board being produced. Second, the bending stiffness is typically different in the machine direction (i.e., along the direction of sheet movement through the board-forming machine) and the cross direction (i.e., perpendicular to the machine direction). Another barrier to the on-line measurement of bending stiffness is that, during the manufacture of paperboard, the board is pulled through the board-forming machine. Accordingly, any on-line stiffness sensor must be capable of distinguishing the inherent resistance to bending of the board structure from resistance to bending resulting from the tension applied to the board.
In the past, laboratory measurements have been used to determine paperboard stiffness in terms of the results of destructive tests, wherein a relatively small elongated sample is cut from the board and subjected to a bending force. For example, one conventional bending stiffness test is called the "Taber stiffness test". In the Taber stiffness test, a strip of paperboard is clamped at one end, hung from the clamp, and subjected to a bending load at the other end. The Taber stiffness value is the average bending moment necessary to deflect the strip 15 degrees from vertical in the two directions perpendicular to the plane of the strip.
There are numerous other standardized bending stiffness measurements in widespread use throughout the paperboard industry. However, to the best of the present inventors' knowledge, all such measurements require manually testing small samples of the board. Accordingly, such tests are destructive as well as labor and time intensive. Needless to say, therefore, none of these tests lend themselves to use in connection with the continuous on-line measurement of board stiffness. However, because of their widespread popularity, any method used to measure on-line bending stiffness should provide results which correlate with the recognized standard tests.
The basic factors governing the stiffness of paperboard sheet are the sheet thickness and the elastic modulus of the sheet. For a unit width of homogenous sheet, the bending stiffness increases with the cube of the caliper according to the following equation: ##EQU1## where, E=elastic modulus;
t=sheet caliper; and PA1 S=bending stiffness.
Thus, the bending stiffness of paperboard is a product of an intrinsic material property, E, and a geometry factor, t.sup.3 /12.
The parameters which affect the elastic modulus, E, include the tree species used in the production of the board fiber, the fiber processing and refining techniques, wet pressing, filler content, calendering and the moisture content of the board. In multi-ply sheets, the arrangement of the various plys and the thickness of each ply will also have a significant effect on bending stiffness.